OnStephani's rotating dust solutions

Some years ago Stephani derived two classes of rotating dust solutions. In this paper Stephani's results are generalised to the case where the cosmological constant is non-zero. The solutions are of Petrov type D and the magnetic part of the Weyl tensor vanishes. The solutions involve seven arbitrary functions of a spacelike coordinate and in general they admit no Killing vectors. Nevertheless the spacetime geometry is relatively simple and admits a foliation of timelike hypersurfaces of constant intrinsic curvature =3 and zero extrinsic curvature. The (geodesic) ow-lines of the uid are tangent to these hypersurfaces and in general the ow is rotating, shearing and expanding. In the vacuum limit the solutions reduce to spacetimes of constant curvature. y